My answer: This question reminds me of the one about how many angels can dance on the head of a pin. The other dimensions in string theory refer to the six space dimensions that are hypothesized to be very tightly wrapped around the three large space dimensions of length, width, and height. Specifically, the extra six space dimensions of string theory must be shaped like a Calabi-Yau manifold. (See the figure below for an artist’s attempt to show a cross section of such a six-dimensional manifold). As I explained in my book, Beyond the Cosmos, 3rd edition, physicists involved these six extra space dimensions as a way to bring consistency to and complete integration of particle physics, cosmology, quantum mechanics, gravity, and general relativity. String theory models are not the only models claiming to produce such consistency and integration. However, all the viable models to date do invoke extra space dimensions.
Figure: Artist’s Depiction of a Multidimensional Calabi-Yau Manifold
Credit: public domain
Many people have further speculated that perhaps in these extra space dimensions is where the angels dwell and where spiritual phenomena emanate. From a biblical perspective, one reason to question such a conclusion is that the angelic realm and the source of spiritual phenomena survives the eradication of the universe and its laws of physics. As God spoke the universe, its laws of physics, and space-time dimensions into existence, a time will come immediately after God permanently eradicates evil when he will speak them out of existence and replace them with a new creation with different laws of physics, and different dimensions. When this future event occurs, we are informed in the Bible that the angels and spiritual phenomena survive this transition. This survival implies that the angelic realm, heaven, hell, and all other possibly existing spiritual realms are in no way constrained by any of the space-time dimensions of the presently existing universe.
Incidentally, the hypothesized six extra space dimensions of string theory are extremely tiny. One can visualize them as akin to 2-dimensional sheets wrapped as very tight scrolls around one of the three large space dimensions of length, width, and height. The cross section of any one of these scrolls would be less than a billionth of a trillionth of the diameter of an electron. If those extra space dimensions really were the angelic realm, I leave it up to my readers to calculate how many quadrillions of angels could dance on the head of a pin.